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A207258 Number of 7 X n 0..1 arrays avoiding 0 0 1 and 1 0 1 horizontally and 0 1 0 and 1 0 1 vertically. 1

%I

%S 42,1764,14406,64176,206514,541380,1231650,2524704,4777290,8483748,

%T 14307678,23117136,36023442,54423684,80047002,115004736,161844522,

%U 223608420,303895158,406926576,537618354,701655108,905569938,1156828512

%N Number of 7 X n 0..1 arrays avoiding 0 0 1 and 1 0 1 horizontally and 0 1 0 and 1 0 1 vertically.

%C Row 7 of A207254.

%H R. H. Hardin, <a href="/A207258/b207258.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/60)*n^7 + (77/20)*n^6 + (2527/60)*n^5 + (119/4)*n^4 - (644/15)*n^3 + (42/5)*n^2 + (4/5)*n.

%F Conjectures from _Colin Barker_, Jun 21 2018: (Start)

%F G.f.: 42*x*(1 + 34*x + 35*x^2 - 96*x^3 + 15*x^4 + 14*x^5 - x^6) / (1 - x)^8.

%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

%F (End)

%e Some solutions for n=4:

%e ..1..0..0..0....1..0..0..0....1..1..1..0....0..0..0..0....1..0..0..0

%e ..1..1..0..0....1..0..0..0....0..1..1..1....0..1..1..1....1..1..0..0

%e ..1..1..0..0....1..0..0..0....0..1..1..1....0..1..1..1....0..1..0..0

%e ..0..1..1..0....0..1..1..0....1..1..0..0....1..1..0..0....0..0..0..0

%e ..0..1..1..0....0..1..1..0....1..0..0..0....1..0..0..0....1..0..0..0

%e ..0..1..0..0....0..1..0..0....0..0..0..0....1..0..0..0....1..1..0..0

%e ..0..1..0..0....0..1..0..0....0..0..0..0....0..1..0..0....0..1..0..0

%Y Cf. A207254.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 16 2012

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Last modified January 16 19:48 EST 2022. Contains 350376 sequences. (Running on oeis4.)